A176010 Positive numbers k such that k^2 == 2 (mod 97).

14, 83, 111, 180, 208, 277, 305, 374, 402, 471, 499, 568, 596, 665, 693, 762, 790, 859, 887, 956, 984, 1053, 1081, 1150, 1178, 1247, 1275, 1344, 1372, 1441, 1469, 1538, 1566, 1635, 1663, 1732, 1760, 1829, 1857, 1926, 1954, 2023, 2051, 2120, 2148, 2217

Offset: 1

Author

Vincenzo Librandi, Apr 06 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Magma

[(-97+41*(-1)^n+194*n)/4: n in [1..50]]; // Vincenzo Librandi, Jul 13 2012

Mathematica

Table[(97-41*(-1)^(n-1)+194*(n-1))/4,{n,1,50}] (* Vincenzo Librandi, Jul 13 2012 *)
Select[Range[2500],PowerMod[#,2,97]==2&] (* or *) LinearRecurrence[{1,1,-1},{14,83,111},50] (* Harvey P. Dale, Mar 28 2024 *)

Formula

a(n) = (-97 + 41*(-1)^n + 194*n)/4.

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3; a(1)=14, a(2)=83, a(3)=111.

a(n) = a(n-1) + 69 for n even, a(n) = a(n-1) + 28 for n odd, a(1)=14.

G.f.: x*(14+69*x+14*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Aug 24 2011

Sum_{n>=1} (-1)^(n+1)/a(n) = cot(14*Pi/97)*Pi/97. - Amiram Eldar, Feb 28 2023